The functions \( f, g \), and \( h \) are defined as follows. \[ f(x)=\frac{5+4 x^{2}}{x^{2}} \quad g(x)=-2|x-3| \quad h(x)=-4+\sqrt{x+18} \] Find \( f(-2), g(-3) \), and \( h(-2) \). Simplify your answers as much as possible. \[ f(-2)=\square \] \( g(-3)=\square \)

To find the values of \( f(-2) \), \( g(-3) \), and \( h(-2) \), we will substitute the respective values into the functions. First, calculating \( f(-2) \): \[ f(x) = \frac{5 + 4x^2}{x^2} \] Substituting \( x = -2 \): \[ f(-2) = \frac{5 + 4(-2)^2}{(-2)^2} = \frac{5 + 4 \cdot 4}{4} = \frac{5 + 16}{4} = \frac{21}{4} \] Next, calculating \( g(-3) \): \[ g(x) = -2|x - 3| \] Substituting \( x = -3 \): \[ g(-3) = -2|-3 - 3| = -2|-6| = -2 \cdot 6 = -12 \] Finally, calculating \( h(-2) \): \[ h(x) = -4 + \sqrt{x + 18} \] Substituting \( x = -2 \): \[ h(-2) = -4 + \sqrt{-2 + 18} = -4 + \sqrt{16} = -4 + 4 = 0 \] To summarize: \[ f(-2) = \frac{21}{4}, \quad g(-3) = -12, \quad h(-2) = 0 \] So the final boxed answers are: \[ f(-2) = \frac{21}{4} \] \[ g(-3) = -12 \]